I'm confused about the nature of antecedents and conditionals like: (i) "Only if A, then B". I was told in my logic class that antecedents are always sufficient conditions and consequents are always necessary conditions. But if that's the case, then the antecedent in (i) "Only if A" is a sufficient condition. Particularly a sufficient condition for B. But saying "Only if A, then B" means that A is a necessary condition for B as well. So it appears that the antecedent in (i) is both a sufficient and necessary condition. But that doesn’t seem right, given that (i) is equivalent to (ii) If B, then A. And this means A is only a necessary but not a sufficient condition for B. Option 1: Maybe antecedents only are sufficient conditions in simple conditionals like (iii) “If A, then B”; but they aren’t sufficient conditions in conditionals like "Only if A, then B". That might be right. Option 2: On the other hand, we might say "Only if A" just seems to be an antecedent but isn't really. That would...

Like you, I'm puzzled by the form of the conditional "Only if A, then B." It doesn't seem to be idiomatic English. One might say "Only if you go to the party will I go," but one wouldn't say "Only if you go to the party, then I will go." That would be unidiomatic. So I presume that the conditional form you're learning is "Only if A, B" rather than "Only if A, then B." I would interpret "Only if A, B" as stating that A is a necessary condition for B, and therefore implying that B is a sufficient condition for A. If one wants to say that A is both necessary and sufficient for B, then one can say "If and only if A, B" -- although "A if and only if B" would be a smoother way of saying it. In any case, make sure that your logic teacher really did say "Only if A, then B" and, if so, ask if he/she meant to say "Only if A, B."

Let ‘B’= to be; let ‘~B’=not to be. P1: B v ~B P2: ~B C: ~B P2 is the negation of the left disjunct in P1, not the affirmation of the right disjunct in P1. P1: To be or not to be. P2: Not to be. C: Not to be. It seems to me that, argumentatively, there’s a difference between affirming ‘not to be’, the right disjunct, and negating ‘to be’, the left disjunct. It just happens that, in this case, what’s affirmed and what’s negated are logically equivalent. Is there a convention for conveying that argumentative difference? Also, can you recommend any articles or books where I can learn more about issues like this? Thank you very much :)

Interesting question! I think you're right that there's something peculiar about this disjunctive syllogism: (1) B v ~ B (2) ~ B (3) ~ B You say that (2) must be the negation of (1)'s left disjunct rather than the assertion of (1)'s right disjunct, even though both of those are syntactically the same. You may find allies in those who distinguish between (i) denying or rejecting a proposition and (ii) asserting the proposition's negation. See Section 2.5 of this SEP entry . But here's a different diagnosis. Although (1)-(3) is a valid argument, and even a valid instance of disjunctive syllogism, the argument is informally defective because premise (1) is superfluous: (1) isn't needed for the argument's validity. Furthermore, anyone justified in asserting (2) is thereby justified in asserting (3) without need of (1). This argument is similar: (4) ~ B v B (5) ~ ~ B (6) B The claim that (5) is the negation of (4)'s left disjunct is at least as plausible as the claim that (2) is the negation of (1...

There is an infinite number of words - "ONE", "TWO", "THREE"... etc. Every word has a definition. Every definition consists of letters. There is a finite number of arrangement of letters; thus there is a finite number of definitions. Thus there is at least one word that doesn't have a definition. Paradox?

There is a finite number of arrangements of letters; thus there is a finite number of definitions. Is that true if we're allowed to use each letter an increasing number of times? If our stock of letter tokens increases without limit, then can't the number (and length) of our definitions also increase without limit? Certainly the names of the numbers will tend to get longer as the numbers they name increase, and those names will reuse letters to an ever-increasing degree.

Say I have a sequence of numbers - 1,2,3,4,5,6,7. I add 1 to 7 to create the next number in the sequence,8. The sequence is finite. I add 1 to 8 to get the next number in the sequence, 9. The sequence is finite. I keep on going... At what point does my sequence become infinite? How can my sequence ever become infinite?

I assume that there's some nonzero minimum time, however brief, that you require to perform each step of addition. In that case, you will never produce an infinite sequence of numbers: that is, there is no finite time at which you will have produced an infinite sequence of numbers. That fact doesn't imply that the positive integers aren't an infinite sequence of numbers -- only that you can't produce them in the described way in a finite amount of time.

Keep in mind I'm a complete novice in philosophy, especially when it comes to the literature. I might misrepresent some positions completely. Please call me out. In short: The determinist states: Our decisions are bound to causation, and thus we are not truly free. This statement implies that the only way for free will to exist would be to detach an agent from causation; as long as some factors affect out motivation to do something, we are not truly free. The determinist thus claims that the only way for a choice to be free is that there would be some force acting above the physical reality, especially when it comes to cognition and decisionmaking. Thus only in a dualistic reality is free will possible. I have a few problems with this: 1. This method of defining free will seems to consequentally destroy the agent. If we were to be able to decide what we want, we'd, at least apparently, fundamentally be nothing. How would it be possible to even assign a different "want" to ourselves without that want...

You wrote, "The determinist states: Our decisions are bound to causation, and thus we are not truly free." In the context of free will, what you say describes not determinists in general but only hard determinists, i.e., those determinists who also say that determinism rules out free will. The other kind of determinists -- soft determinists -- accept determinism but say that it doesn't rule out free will and may indeed be essential to acting freely. Unlike hard determinists, soft determinists allow for the combination of determinism, free will, and moral responsibility. You'll find details in this SEP entry .

Hi, While reading aristotle and aquinas on part whole relationship i often read the phrase "something qua itself and qua something else" as in man qua headed or qua an animal, what do they mean by that ? and how can something be qua itself and at the same time be as something else ? Isnt that a contardiction ? Thanks in advance

In this context, it sounds as though "qua" is being used to mean "considered as." So, for example, qua sentient being (i.e., considered as a sentient being) you have particular rights, while qua adult citizen (i.e., considered as an adult citizen) you have those rights plus additional rights, such as the right to vote. I see no contradiction here.

Fred is 14. Would you agree that Fred isn't in the set of people aged less than 15 because he's 14, he's in the set of people aged less than 15 because he's less than 15? (It doesn't matter what his age is, as long as he's less than 15.)

I doubt that "because" is as finicky as you seem to be suggesting it is. I think it's perfectly true that Fred belongs to the set because he is only 14, and it's perfectly true that Fred belongs to the set because he is less than 15. I'm not familiar with any explanatory concept according to which one of those facts about Fred, but not the other, explains Fred's membership in the set. In any case, I'm confident that "because" does not stand for any such concept.

No two sets can have the same conditions for membership, so if Miss X is in the set of young girls because she's a young girl, then she cannot be in the set of female humans because she's a young girl. Paradox?

If there is a paradox here, I don't think it will have anything to do with a conflict in the conditions for set membership. Let's leave aside that there may be sorites-style paradoxes arising from the vagueness of the predicates "young girl" and even "female human." I suspect that those paradoxes can be solved in the "epistemicist" way (see this link ). One and the same individual can possess various mutually consistent properties: she can be a young girl (at a specified time t ), a female human being (at any time during her existence, including at time t ), and so on. So Miss X can belong to the set of girls who are young at t , the set of female human beings, the set of human beings, the set of mammals, the set of things referred to by you in your question above, etc. She would belong to each of those different sets for different but compatible reasons. I don't see anything paradoxical about that.

I wonder about the nature of modal concepts such as necessity and possibility. When I say "It is possible that this page is white" or "it is necessary that two plus two equals four" I use modal words in my speech. Where do these concepts belong to? Are they in my mind or I receive them from the objects themselves?

It's a good idea to distinguish between epistemic uses of modal language (which have to do with our knowledge) and alethic uses (which have to do with truth independently of our knowledge). When you say, "It is possible that this page is white," you might be wearing tinted glasses and simply admitting that, for all you know, the page that looks amber to you is in fact white (i.e., it looks white to normal observers in normal conditions). That use of "possible" would be epistemic. Or, instead, you might be saying that the page, which in fact emerged a mottled gray from the unreliable paper mill, could have been white had the mill done a better job. Or you might simply infer from the fact that the page is white that it's possible that the page is white: what is true is of course also possible. Those uses of "possible" would be alethic. Where do alethic modal concepts belong? I'd say that they belong to logic, in the sense that they are at the foundation of the concept of logical consequence. To...

What purpose does humanity as a whole serve? Considering that the majority of people in this world struggle just to survive on a day-to-day basis, and that those in developed countries struggle to maintain the status quo or at best to improve their lot in life, what purpose do we serve? Very few of us have our needs met in such a way that we can devote all our time to pursuits of thought and charity, and of those few who meet the criteria, fewer still can be bothered to devote their time to the betterment of humanity. I see no useful purpose to humanity as a whole and in fact see humanity as a blight & plague upon the world. We can't survive with the nature around us, in terms of food, but nature can not only survive without humans, but would actually be better off without us; so what use is humanity to the world around us, and what, if any, purpose does humanity serve? #InquirinMindsWannaKnow

Humans comprise a naturally occurring species, so I would ask, "What purpose could any naturally occurring species serve?" We humans use some naturally occurring species, such as Oncorhynchus nerka (sockeye salmon), as food, but it doesn't follow that the purpose of that species is to be our food. Unless there is a god who created species for this or that purpose, naturally occurring species -- qua species -- have no purposes. Whatever has a purpose must be intentionally given that purpose, and I think that no being exists who could give humanity as a whole a purpose. So I agree with you that humanity as a whole has no purpose. But humans are hardly unique in that way. Moreover, even if there were a being who created all humans for a purpose, I doubt that any humans (much less all of humanity) would thereby acquire that purpose, as I suggested in my answer to Question 27543 . The only way I can see in which humanity as a whole could have a purpose would be if all humans collectively...

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